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A Contribution To Modern Data Reduction Techniques And Their Applications By Applied Mathematics And Statistical Learning

High-dimensional data take place from digital image processing, gene expression micro arrays, neuronal population activities to financial time series. Dimensionality Reduction - extracting low dimensional structure from high dimension - is a key problem in many areas like information processing, machine learning, data mining, information retrieval and pattern recognition, where we find some data reduction techniques. In this thesis we will give a survey about modern data
reduction techniques, representing the state-of-the-art of theory, methods and application, by introducing the language of mathematics there. This needs a special care concerning the questions of, e.g., how to understand discrete structures as manifolds, to identify their structure, preparing the dimension reduction, and to face complexity in the algorithmically methods. A special emphasis will be paid to Principal Component Analysis, Locally Linear Embedding and Isomap Algorithms. These algorithms are studied by a research group from Vilnius, Lithuania and Zeev Volkovich, from Software Engineering Department, ORT Braude College of Engineering, Karmiel, and others. The main purpose of this study is to compare the results of the three
of the algorithms. While the comparison is beeing made we will focus the results and duration.

Identiferoai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12612819/index.pdf
Date01 January 2010
CreatorsSakarya, Hatice
ContributorsWeber, Gerhard Wilhelm
PublisherMETU
Source SetsMiddle East Technical Univ.
LanguageEnglish
Detected LanguageEnglish
TypeM.S. Thesis
Formattext/pdf
RightsTo liberate the content for public access

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